Measurement of the $B^{0} - \overline{B}^{0}$ mixing frequency $\Delta m_{d}$ in the decay channel $B^{0} \rightarrow D^{-}(\rightarrow K^{+} \pi^{-} \pi^{-}) \mu^{+} X$ at the LHCb experiment

This thesis presents a measurement of the $B^{0} - \overline{B}^{0}$ mixing frequency $\Delta m_{d}$, using the semileptonic decay channel $B^{0} \rightarrow D^{-}(\rightarrow K^{+} \pi^{-} \pi^{-}) \mu^{+} X$. Semileptonic decays are not fully reconstructed due the non-detection of neutrinos. In this analysis a new approach is used to account for the missing reconstructed $B^{0}$ momentum caused by this. Applying this approach to the measurement of $\Delta m_{d}$ will allow for the extraction of its value with high precision. The dataset used in this analysis was collected by the LHCb experiment in 2011 and corresponds to an integrated luminosity of ${\cal L}=1.0 fb^{-1}$. The value of $\Delta m_{d}$ is extracted from a three-dimensional maximum-likelihood fit. This fit uses information about the mixing state of the \Bz meson and the distributions of the reconstructed $B^{0}$ decay time and the invariant $D^{-}$ mass. The result of this analysis is a new measurement of the mixing frequency $\Delta m_{d} = (0.5103 \pm 0.0065({\rm stat.}) \pm 0.0046({\rm syst.}))ps^{-1}$. This is in good agreement with the existing world average. This measurement is the first step of the measurement of the mixing asymmetry $a_{sl}^{d}$. Investigating this asymmetry is a way to probe CP violation and search for New Physics.